Question

in the figure below, find the exact value of x. (do not approximate your answer.)

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if an altitude is drawn from the right - angle vertex to the hypotenuse, then the length of a leg of the right - triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg. Here, we have the relationship $4^{2}=5x$.

Step2: Solve for x

We start with the equation $16 = 5x$. Then, by dividing both sides of the equation by 5, we get $x=\frac{16}{5}$.

Answer:

$x=\frac{16}{5}$